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Ulleksa [173]
3 years ago
5

An old house in Pomona, CA is inhabited by a variety of ghosts. Ghost appearances occur in the house according to a Poisson proc

ess having a rate of 1.4 ghosts per hour. A professor from Cal Poly Pomona has developed a device that can be used to detect ghost appearances. Suppose it is now 1:00 p.m. and the last ghost appearance (the 6th overall) was at 12:35 p.m.
What is the probability that the 7th ghost will appear before 1:30 p.m., to the nearest three decimal places?
Mathematics
1 answer:
shutvik [7]3 years ago
8 0

Answer:

The probability is 0.503

Step-by-step explanation:

If the ghost appearances occur in the house according to a Poisson process with mean m, the time between appearances follows a exponential distribution with mean 1/m. so, the probability that the next ghost appearance happens before x hours is equal to:

P(X\leq x)=1-e^{-xm}

Then, replacing m by 1.4 ghosts per hour we get:

P(X\leq x)=1-e^{-1.4x}

Additionally, The exponential distribution have a memoryless property, so if it is now 1:00 p.m. and we want the probability that ghost appear before 1:30 p.m., we need to find the difference in hours from 1:00 p.m and 1:30 p.m. no matter that the last ghost appearance was at 12:35 p.m.

Therefore, there are 0.5 hours between 1:00 p.m. and 1:30 p.m, so the probability that the 7th ghost will appear before 1:30 p.m is calculated as:

P(x\leq 0.5)=1-e^{-1.4*0.5} =0.503

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Mark can remember only the first 4 digits of his friend's phone number. He also knows that the number has 7 digits and that the
denis-greek [22]

Answer:

<em>19800 seconds, or 330 minutes, or 5 hours + 30 minutes</em>

Step-by-step explanation:

<u>Number Permutations</u>

We know the phone number has 7 digits, 4 of which are known by Mark. This leaves him 3 digits to guess with. We also know the last one is not zero. The number can be represented as

XXY

Where X can be any digit from 0 to 9 and Y can be any digit from 1 to 9. The first two can be combined in 10x10 ways, and the last one can be of 9 ways, this gives us 10x10x9 = 900 possible permutations.

If each possible number takes him 22 seconds, every possibility will need

22x900=19800 seconds, or 330 minutes, or 5 hours + 30 minutes

3 0
2 years ago
Which of the following are solutions to 2x^2-8x-90? select all that apply.
Lyrx [107]
<span>Simplifying:
2x2 + -8x + -90 = 0

Reorder the terms:
-90 + -8x + 2x2 = 0

Solving
-90 + -8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -4x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
Subproblem 1:

Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms:
-5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5

Combine like terms:
0 + 5 = 5 -1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2:

Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms:
9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9

Combine like terms:
0 + -9 = -9 -1x = -9

Divide each side by '-1'.
x = 9

Simplifying x = 9

Solution
x = {-5, 9}</span>
8 0
2 years ago
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